Problem: Solve for $x$ and $y$ using elimination. ${-3x-3y = -18}$ ${-2x-3y = -14}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${-3x-3y = -18}$ $2x+3y = 14$ Add the top and bottom equations together. $-x = -4$ $\dfrac{-x}{{-1}} = \dfrac{-4}{{-1}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {-3x-3y = -18}\thinspace$ to find $y$ ${-3}{(4)}{ - 3y = -18}$ $-12-3y = -18$ $-12{+12} - 3y = -18{+12}$ $-3y = -6$ $\dfrac{-3y}{{-3}} = \dfrac{-6}{{-3}}$ ${y = 2}$ You can also plug ${x = 4}$ into $\thinspace {-2x-3y = -14}\thinspace$ and get the same answer for $y$ : ${-2}{(4)}{ - 3y = -14}$ ${y = 2}$